How is a compensated demand curve different from an ordinary demand curve? Why must the law of demand always hold for one while it may be violated for the other?

What will be an ideal response?

An ordinary demand curve shows how the quantity demanded at the optimum changes in reaction to a change in price. The change in quantity demanded is decomposed into substitution and income effects, and the compensated demand curve shows only how the substitution effects of price changes affect quantity demanded. Briefly, ordinary demand curves include both substitution and income effects, while compensated demand curves contain only substitution effects and no income effects. Substitution effects always support the law of demand since indifference curves are convex, but income effects will be in opposition to the law of demand if the good is inferior. Thus the law of demand must hold for compensated demand curves since they contain only substitution effects. On the other hand, the law of demand may be violated for the ordinary demand curves which include income effects-this happens when the good is inferior and the income effect outweighs the substitution effect.